{
  "id": "1402.1441",
  "version": "v2",
  "published": "2014-02-06T18:03:29.000Z",
  "updated": "2015-01-08T17:30:22.000Z",
  "title": "The shape of expansion induced by a line with fast diffusion in Fisher-KPP equations",
  "authors": [
    "Henri Berestycki",
    "Jean-Michel Roquejoffre",
    "Luca Rossi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish a new property of Fisher-KPP type propagation in a plane, in the presence of a line with fast diffusion. We prove that the line enhances the asymptotic speed of propagation in a cone of directions. Past the critical angle given by this cone, the asymptotic speed of propagation coincides with the classical Fisher-KPP invasion speed. Several qualitative properties are further derived, such as the limiting behaviour when the diffusion on the line goes to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-06T18:03:29.000Z",
      "abstract": "In this paper, we establish a new property of Fisher-KPP type propagation in a plane, in the presence of a line with fast diffusion. We prove that there is a critical angle such that the line enhances the asymptotic speed of propagation in a cone of directions. Past this critical angle, the asymptotic speed of propagation coincides with the classical Fisher-KPP invasion speed. Several qualitative properties are further derived, such as the limiting behaviour when the diffusion on the line goes to infinity.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-08T17:30:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fast diffusion",
      "fisher-kpp equations",
      "fisher-kpp type propagation",
      "critical angle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.1441B"
    }
  }
}